Medical equipment for radiation therapy treats tumorous tissue with high-energy radiation. The amount of radiation and its placement must be accurately controlled to ensure both that the tumor receives sufficient radiation to be destroyed, and that the damage to the surrounding and adjacent non-tumorous tissue is minimized.
External source radiation therapy uses a radiation source external to the patient to treat internal tumors. The source of high-energy radiation may be x-rays, or electrons from linear accelerators in the range of 2 to 25 MeV, or gamma rays from highly focused radioisotopes such as a Co.sup.60 source having an energy of 1.25 MeV.
The external source is normally collimated to direct a beam only to the tumorous site. Typically, the tumor will be treated from several different angles with the intensity and shape of the beam adjusted appropriately. Using multiple beams which converge on the site of the tumor reduces the dose to particular areas of the surrounding tissue. The angles at which the tumor is irradiated may be further selected to avoid the irradiation of radiation sensitive structures near the tumor site.
A highly accurate method of controlling the dose to a patient employs a radiation source that produces a fan beam composed of many individual rays whose intensity may be independently controlled. The fan beam orbits the patient within a slice plane illuminating a slice of the patient while the intensity of each ray of the fan beam is changed as a function of that angle. By properly selecting the beam intensities at different angles, complex regions within the slice may be accurately irradiated. U.S. Pat. No. 5,317,616, issued May 31, 1994 and assigned to the same assignee as the present application, describes the construction of one such machine and one method of calculating the necessary beam intensities as a function of angle.
As mentioned, with such machines, the dose at any given volume within the patient will be derived from a number of different beams irradiating that volume at different angles. Each beam passes both through the tumor and through tissue on either side of the area to be irradiated. Beams which pass through tissue flanking the tumor and highly sensitive to radiation, are decreased in intensity. Other beams passing through less sensitive tissue are increased in intensity to maintain the dose to the tumor.
Determining beam weights for a desired dose pattern is normally done by an iterative technique, where particular beam weightings are evaluated by mathematically modeling the expected dose. The beam weights are then adjusted and the model is evaluated to see if it is closer to the desired dose. This process is repeated many times until the computed dose pattern closely approximates the desired dose pattern. The resulting beam weights are recorded and used for the radiation therapy. Generally, the changes in the beam weights between iterations are random and hence the process may be broadly characterized as stochastic.
In a "simulated annealing" stochastic technique, (so-called because of its mathematical similarity to the process of annealing metal) a new set of beam weights is always adopted, in the iterative process, if it results in an improvement in the computed dose distribution d as measured by a figure of merit of the computed dose f(d) called the "objective function". On the other hand, a new set of beam weights which results in a worse computed dose than the previous result may be adopted with a small probability. This probability is expressed by the function exp(-.DELTA.f(a)/T), where .DELTA.f(a) is the change in the objective function from one iteration to the next, and T, called the "temperature" is progressively reduced as the number of iterations increases, thereby reducing the probability of accepting worse solutions as measured by the objective function. The purpose of probabilistically accepting worse solutions is to allow the iterative procedure to escape from "local minima" of the objective function space, (corresponding to locally optimal solutions) and to continue onward toward determining the best possible solution associated with the smallest objective function, commonly referred to as the "global minimum". See, generally, Webb, S. Optimization by Simulation Annealing of Three Dimensional Conformal Treatment planning for Radiation Fields Defined by a Multi-Leaf Collimator, Phys. Med. Biol. 36 1201-26, 1991.
Another stochastic technique is the so-called "genetic algorithm". During each iteration, the genetic algorithm samples a population of solutions from which a subpopulation of best solutions is chosen based on the match between the computed dose and the desired dose. A new population of solutions is bred from random pairs of members of the subpopulation using techniques called "cross over" and "mutation." The population of solutions rapidly "evolves" towards one whose members, although not necessarily identical, share many characteristics of the globally optimal solution. See, generally, Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison Wesley (1989).
Millions of iterations may be required to reach acceptable solutions with these techniques. As a result, the radiation planning process is delayed and the planning physician is discouraged from varying the initially selected dose pattern by the lengthy time needed for a recalculation.